The appropriate EFT for low-energy physics is an extension of the SM called SMEFT, in which the effective operators contain SM fields only, and new physics enters through the Wilson coefficients of these operators. However, this approach cannot provide a meaningful description of the on-shell decays of a new heavy resonances. The scale separation in this case is between the energy injected into the final-state particles and their mass, \(E_i\sim m_V\gg m_i\) , where \(i\)  labels the final-state particles. The appropriate framework for this situation is Soft-Collinear Effective Theory (SCET) [1]}, [2]}, [3]}, [4]}, an effective theory for highly energetic light particles. In SCET every SM field is split up into momentum modes that are either collinear with an energetic final-state particle or soft. Modes with large virtualities are integrated out in the Wilsonian way. The effective theory is built from gauge-invariant building blocks, which are comprised of the soft and collinear fields dressed with Wilson lines.
